Melt the butter in a large frying pan and cook the leeks for 4–5 minutes, until softened.
Meanwhile, roll out the pastry on a lightly floured work surface and stamp out 4 x 22 cm (8½ inch) circles.
Transfer the leeks to a large bowl, add the tuna, potato, cheese, chives and a pinch of salt and pepper and mix well.
Spoon the mixture into the middle of each pastry circle, then brush a little beaten egg around the border. Fold up the pastry, pinching and crimping the edges together along the top to encase the filling.
Arrange the pasties on the prepared baking sheet, brush with beaten egg and bake in a preheated oven, 220˚C (425˚F), Gas Mark 7, for about 15 minutes, or until puffed and golden. Cool slightly and serve with salad leaves, if desired.